Pair distribution function

For a fluid of $N$ particles, enclosed in a volume $V$ at a given temperature $T$ (canonical ensemble) interacting via the `central' potential $\Phi (r)$, the two particle distribution function is defined as

${\rm {g}}_{N}^{(2)}(r_{1},r_{2})=V^{2}{\frac {\int ...\int e^{-\beta \Phi (r_{1},...,r_{N})}{\rm {d}}r_{3}...{\rm {d}}r_{N}}{\int e^{-\beta \Phi (r_{1},...,r_{N}){\rm {d}}r_{1}...{\rm {d}}r_{N}}}}$

See also

• Compressibility equation
• Pressure equation
• Energy equation